Search results for "Bounded function"
showing 10 items of 508 documents
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence
2014
Abstract. We consider the following problem: given a bounded convex domain Ω ⊂ ℝ N ${\Omega \subset \mathbb {R}^N}$ we consider the limit as p → ∞ of solutions to - div ( b p - p | D u | p - 2 D u ) = f + - f - ${- \operatorname{div} (b_{p}^{-p} |Du|^{p-2} Du)=f_+ - f_-}$ in Ω and b p - p | D u | p - 2 ∂ u ∂ η = 0 ${ b_{p}^{-p} |Du|^{p-2} \frac{\partial u}{\partial \eta }=0}$ on ∂ Ω ${\partial \Omega }$ . Under appropriate assumptions on the coefficients bp that in particular verify that lim p → ∞ b p = b ${ \lim _{p\rightarrow \infty } b_p = b }$ uniformly in Ω ¯ ${\overline{\Omega }}$ , we prove that there is a uniform limit of u p j ${u_{p_j}}$ (along a sequence p j → ∞ ${p_j \rightarrow…
High-pressure Raman investigation of high index facets bounded alpha-Fe2O3 pseudocubic crystals
2021
[EN] High index facet bounded alpha-Fe2O3 pseudocubic crystals has gained the attention of the scientific community due to its promising electrochemical sensing response towards aqueous ammonia. The structural stability of alpha-Fe2O3 pseudocubic crystals is investigated through high-pressure Raman spectroscopy up to 22.2 GPa, and those results are compared with our ab initio theoretical calculations. The symmetry of the experimental Raman-active modes has been assigned by comparison with theoretical data. In addition to the Raman-active modes, two additional Raman features are also detected, whose intensity increases with compression. The origin of these two additional peaks addressed in t…
Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies
1999
We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We c…
ON SOLVABILITY OF THE DAMPED FUČÍK TYPE PROBLEM WITH INTEGRAL CONDITION
2014
The solvability results are established for the boundary value problem with a damping term , x(0) = 0, where x + = max{x, 0}, x - = max{-x, 0}, h is a bounded nonlinearity, µ, λ real parameters. The existence results are based of the knowledge of the Fučík type spectrum for the problem with h ≡ 0
The guarded fragment with transitive guards
2004
The guarded fragment with transitive guards, (GF+TG), is an extension of the guarded frag- ment of 9rst-order logic, GF, in which certain predicates are required to be transitive, transitive predicate letters appear only in guards of the quanti9ers and the equality symbol may appear everywhere. We prove that the decision problem for (GF+TG) is decidable. Moreover, we show that the problem is in 2EXPTIME. This result is optimal since the satis9ability problem for GF is 2EXPTIME-complete (J. Symbolic Logic 64 (1999) 1719-1742). We also show that the satis- 9ability problem for two-variable (GF+TG) is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satis9ability …
An exact algorithm for the min-cost network containment problem
2004
A network design problem which arises in the distribution of a public utility provided by several competitive suppliers is studied. The problem addressed is that of determining minimum-cost (generalized) arc capacities in order to accommodate any demand between given source–sink pairs of nodes, where demands are assumed to fall within predetermined ranges. Feasible flows are initially considered as simply bounded by the usual arc capacity constraints. Then, more general linear constraints are introduced which may limit the weighted sum of the flows on some subsets of arcs. An exact cutting plane algorithm is presented for solving both of the above cases and some computational results are re…
Robust control of production-distribution systems
2007
A class of production-distribution problems with unknown-but-bounded uncertain demand is considered. At each time, the demand is unknown but each of its components is assumed to belong to an assigned interval. Furthermore, the system has production and transportation capacity constraints. We face the problem of finding a control strategy that keeps the storage levels bounded. We also deal with the case in which storage level bounds are assigned and the controller must keep the state within these bounds. Both discrete and continuous time models are considered. We provide basic necessary and sufficient conditions for the existence of such strategies. We propose several possible feedback contr…
Learning for allocations in the long-run average core of dynamical cooperative TU games
2011
We consider repeated coalitional TU games characterized by unknown but bounded and time-varying coalitions' values. We build upon the assumption that the Game Designer uses a vague measure of the extra reward that each coalition has received up to the current time to learn on how to re-adjust the allocations among the players. As main result, we present an allocation rule based on the extra reward variable that converges with probability one to the core of the long-run average game. Analogies with stochastic stability theory are put in evidence.
Power allocation in multi-channel cognitive radio networks with channel assembling
2011
Accepted version of a paper in the book: 2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). Published version available from the IEEE:http://dx.doi.org/10.1109/SPAWC.2011.5990485 Consider power allocation for Secondary User (SU) packet transmissions over multiple channels with variable Primary User (PU) arrival rates in cognitive radio networks. Two problems are studied in this paper: The first one is to minimize the collision probability with PUs and the second one is to maximize the data rate while keeping the collision probability bounded. It is shown that the optimal solution for the first problem is to allocate all power onto the bes…
Dealing with uncertainty in consensus protocols
2009
Recent results on consensus protocols for networks are presented. The basic tools and the main contribution available in the literature are considered, together with some of the related challenging aspects: estimation in networks and how to deal with disturbances is considered. Motivated by applications to sensor, peer-to-peer, and ad hoc networks, many papers have considered the problem of estimation in a consensus fashion. Here, the Unknown But Bounded (UBB) noise affecting the network is addressed in details. Because of the presence of UBB disturbances convergence to equilibria with all equal components is, in general, not possible. The solution of the e-consensus problem, where the stat…